Matematika

Pertanyaan

jika y=x²+2x per x-3 maka y' = ......
pake cara ya☺

1 Jawaban

  • y = (x^2 + 2x)/(x - 3) = u/v
    u = x^2 + 2x => u' = 2x + 2
    v = x - 3 => v' = 1
    y' = (u' v - v' u)/v^2
    = ((2x + 2)(x - 3) - 1(x^2 + 2x)) / (x - 3)^2
    = (2x^2 - 6x + 2x - 6 - x^2 - 2x) / (x - 3)^2
    = (x^2 - 6x - 6) / (x - 3)^2

    = (x^2 - 6x - 6) / (x^2 - 6x + 9)

    ^ = pangkat

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